Transition layer thickness in a fluid-porous medium of multi-sized spherical beads

Momentum and mass transfer at fluid–porous interfaces occur in many technical and natural applications. The vertical extend below a fluid–porous interface within which the free fluid velocity reduces to a constant Darcy velocity in the porous medium is known as Brinkman layer. Recently, the Brinkman layer thickness (δ) has been measured for a porous bed of mono-sized spherical beads, and was found to be in the order of the particle diameter (d). In this study, we investigate a porous medium made of multi-sized spherical beads. The measured averaged interfacial velocity field clearly indicated that, in the case of multi-sized beads, δ is in the order of a characteristic diameter given by (∑ᵢ xᵢ/dᵢ)/(∑ᵢ xᵢ/dᵢ²) with x i and d i being the weight fraction and diameter of the component i in the mixture.